You said 'gen 1' that is a SBC. most people don't care that much. SBC, 1pc or 2pc RMS is about all is usually mentioned regarding SBC. The opti'd LT 1 motors are usually called LT1s, that only bothers the guys with the original solid lifter LT1s, but its fun to bother numbers guys lol. In any event its a 350.
yeah i guess it can matter, but only so to some. i don't see 3rd gen guys crying if i call their engine a 350 and not an L98. once the engine is changed or modified i think it matters less. except when ordering parts!
An LS6 is a BBC!